\section{An Introduction To Grassmann Variables}

We want to have variables which satisfy the relation
\begin{equation}\label{generalizationOfCliffordAlgebras}
\varepsilon^i\varepsilon^j=-\varepsilon^j\varepsilon^i
\end{equation}
which implies when $i=j$ that
\begin{equation}\label{ourCondition}
(\varepsilon^i)^2=0.
\end{equation}
So we basically will have variables that look like
\begin{equation}
a_{0} + \sum_{i}b_{i}\varepsilon^{i} + \sum{i,j}c_{ij}\varepsilon^{i}\varepsilon^{j} + \ldots
\end{equation}
where $a_0$, $b_i$, $c_ij$, etc. are coefficients. By our condition (\ref{ourCondition})
we see that we can have at most, with n different grassmann ``generators''
(meaning we have $\varepsilon^i$ and $i=1,...,n$), we can have 
\begin{equation}
1 + \begin{pmatrix}n\\1\end{pmatrix} + \begin{pmatrix}n\\2\end{pmatrix} + \ldots
= n^2
\end{equation}
terms total, where
\begin{equation}
\begin{pmatrix}n\\k\end{pmatrix} = \frac{n!}{(n-k)!k!}
\end{equation}
is the binomial coefficients.
